When I sit down to prototype something new I always find myself looking up the same snippets to do the same types of things. I figured I might as well record them somewhere so I know an easy place to look when I do forget. All the samples will be in Javascript and should be able to be easily converted to any other language.

**Distance Formula**

Obviously a pretty important one, used to tell the distance between 2 objects. Can be used for simple radius collisions as well.

var distance = Math.sqrt((x2 - x1) *(x2-x1) + (y2 - y1) * (y2-y1));

**Move toward an object (Without rotation) with easing**

x += (targetX-x)/speed; y += (targetY-y)/speed;

**Angle Based Movement**

I always see myself needing this one, whether its for an Asteroids clone, or a follow the leader type game.

velX = Math.cos((angle * Math.PI / 180) * thrust); velY = Math.sin((angle * Math.PI / 180) * thrust);

**Friction**

How do I make something slow down if no force is applied?

velX *= .98; //Any val under 1 is suitable for your needs velY *= .98

**2D Matrix**

This is a pretty simple one I know.. but I always seem to forget it. This is how to store a 2d matrix in an array. And how to find a value you need.

// 2d matrix[y * width + x] var arr = [], width = 10; for(x=0; x<width; x++){ for(y=0; y<width; y++){ arr[y * 10 + x] = x + y; //Or whatever value you need to assign } } //Retrieve a value from x:5, y:2 var val = arr[2 * 10 + 5]; //get the x and y from a 1d array var index = 12, x = index % width, // 2 y = Math.floor(index / width); // 1

**Move towards and object at a constant speed**

var tx = targetX - x, ty = targetY - y, dist = Math.sqrt(tx*tx+ty*ty), rad = Math.atan2(ty,tx), angle = rad/Math.PI * 180;; velX = (tx/dist)*thrust; velY = (ty/dist)*thrust;

**Project a point in front of an object**

x + length * Math.cos(angle*Math.PI / 180); y + length * Math.sin(angle*Math.PI / 180);

**Get the angle between objects**

var x = targetX - this.x, y = targetY - this.y; return Math.atan2(x,-y);

**Plot points around a circle**

var rad = 500, total = 50, centerX = 250, centerY = 250; for(var i = 0; i < total; i++){ ctx.beginPath(); ctx.moveTo(centerX,centerX); var x = centerX + rad * Math.cos(2 * Math.PI * i / total), y = centerY + rad * Math.sin(2 * Math.PI * i / total); ctx.lineTo(x, y); ctx.stroke(); ctx.closePath(); }